1. Field of the Invention
The present invention relates to automatic color photographic printers having settable matrix exposure control computers. More specifically, the invention relates to a method and apparatus for adjusting the settable matrix in such printers.
2. Description of the Prior Art
U.S. Pat. No. 3,120,782 issued Feb. 11, 1964 to Goddard and Huboi discloses an exposure determination system for a color photographic printer that is based on a linear combination of red, green, and blue large area transmission densities (LATD's). For an explanation of LATD and a general introduction to the discussion that follows, see the SPSE Handbook of Photographic Science and Engineering, Wiley and Sons 1973, pages 461-468. In such a printer, the red exposure, for example, is computed as a function of all three (i.e. red, green, and blue) LATD's rather than being based on a measurement of the red LATD alone.
If the characteristics of the printing filters are similar to the responses of the color channels of the densitometer portion of such a printer, the printing densities relate linearly to the measurements made by the densitometer portion of the printer and can be expressed in matrix form as follows: EQU [D]=[P] [C] ([LATD]-[LATD]) (1)
where:
[D]--is a 3.times.1 column vector having elements d.sub.I representing Printing Densities in a Red, Green, Blue coordinate system; PA1 [P]--is a 3.times.3 matrix of elements p.sub.ij relating Integral Densities to Printing Densities; PA1 [C]--is a 3.times.3 diagonal matrix of elements c.sub.ij relating Densitometer Voltages to Integral Densities; PA1 [LATD]--is a 3.times.1 column vector having elements LATD.sub.i representing the Densitometer Voltages generated by the Red, Green, and Blue color channels of the densitometer portion of the printer; and PA1 [LATD]--is a 3.times.1 column vector having elements LATD.sub.i representing the Densitometer Voltages of the calibration original, the calibration original representing some standard such as the center of the population of originals to be printed. PA1 [log E]--is a 3.times.1 column vector having elements logE.sub.i representing the Log Source Exposures of the exposure portion of the printer, i.e., the exposures impinging upon the original, expressed in a Red, Green, Blue coordinate system; PA1 [K]--is a 3.times.1 column vector having elements k.sub.i representing the average Log Exposures or aim points for the population of originals being printed; PA1 [D]--is a 3.times.1 column vector having elements d.sub.i representing the Printing Densities calculated in equation (1); and PA1 [A]--is a 3.times.3 matrix of elements a.sub.ij relating the Log Exposures to the Printing Densities. ##EQU1## PA1 a.sub.ij are the correction matrix elements, i.noteq.j.noteq.k and PA1 Cc.sub.i are the Red, Green, and Blue Chromaticity Correction Levels. PA1 where [Q] is a 3.times.3 matrix of elements ##EQU6##
The exposure equations for such a printer take the following form: EQU [log E]=[K]+[A] [D] (2)
where:
The matrix [A] is called the correction matrix of the printer and will generally have off-diagonal elements. Matrix [A] is physically embodied in the printer described in U.S. Pat. No. 3,120,782 as a matrix of operational amplifiers and variable resistors. The elements a.sub.ij of the correction matrix are adjustable by changing the values or responses of the electronic components comprising the matrix. For this reason, such a printer is called a settable matrix printer. In another type of settable matrix printer, the matrix is stored in digital form in the memory of a digital computer associated with the printer. The exposure control equations are solved by the digital computer, and the results are used to control the exposure portion of the printer. An example of such a printer is the Eastman Kodak Company 2610 Color Printer.
In a settable matrix printer, the correction matrix [A] is said to be a zero correction matrix if measured differences in LATD's, from original to original, result in corresponding changes of comparable magnitude in the resulting prints. Thus if matrix [A] is a zero correction matrix, the log exposures will be equal to the aim points k.sub.i of the exposure equations (2), and the correction matrix [A] will approach a null matrix, i.e., all elements approach zero.
A full correction matrix is defined as one that results in all originals being printed so that there is no variation in the average overall densities in the resulting prints. In such a case, the correction matrix [A] would approach a unit diagonal matrix, i.e., elements a.sub.11, a.sub.22, and a.sub.33 would approach unity, and all other elements would approach zero.
Full correction is desirable to compensate for unwanted variations in LATD's caused by such things as film keeping, incorrect exposure, and improper match between illuminant and film balance (e.g., exposing daylight film under tungsten lighting conditions). However, for those cases where the variations in LATD are due solely to the content of the original scene (commonly called subject failure scenes because they disobey the basic assumption that all scenes integrate to a shade near grey), a zero correction matrix is desirable. The zero correction matrix is needed so that unwanted color shifts in the resulting print will not be introduced by the corrective action of the printer.
One approach to resolving these conflicting requirements for zero and full correction has been to adjust the values of matrix elements a.sub.ij in correction matrix [A] so that the printer will operate at some compromise correction between full and zero. For a discussion of optimum correction for photographic printers in general, see the Article published by Bartelson and HuboI in the Journal of the Society of Motion Picture and Television Engineers, Vol. 65, pages 205-215, 1956. As is pointed out in the Bartelson and HuboI article, the optimum correction level is a function of the population of negatives being printed and varies for different negative populations.
In order to explain the prior art methods for adjusting the matrix elements in the printer correction matrix [A], it would first be helpful to expand upon the concept of printer correction that has been discussed above.
In general, "correction level" may be defined as the rate of change of a given component of source exposure with respect to some related change in a component of the density of the original. If the exposure equation (2) is rewritten to represent changes, it appears as follows: EQU [.DELTA.logE]=[A] [.DELTA. D] (3)
it is seen that in the general sense, the matrix elements a.sub.ij are correction levels since they relate changes in components of log source exposure (.DELTA.logE.sub.i) to some changes in components of the measured density of the original (.DELTA.D.sub.i). For example, element a.sub.11 relates the change in red log exposure to a change in red density; a.sub.21 relates the change in green log exposure to a change in red density, etc. The relationships or correction levels defined by the elements of matrix [A], however, do not coincide with any intuitive concept of correcting the exposure of a print.
The traditional subjective criteria for evaluating color prints have been neutral density (i.e., is the overall print too light or too dark), color balance or hue (i.e., do the colors in the print appear as the scene is remembered) and saturation or pureness of the color (i.e., are the colors bright and pure, or are they grey and muddy).
The primary additive colors can be thought of in terms of an orthogonal 3 dimensional coordinate system with axes labeled R, G, and B (see FIG. 1). The traditional subjective criteria for judging color prints may be described in a new coordinate system defined in the following way. A Neutral axis N is defined as R=G=B. At any given point on the Neutral axis N, a plane perpendicular to the axis N is called a chromaticity plane and the projection of the R, G, B axes onto the chromaticity plane are called the Red, Green, and Blue chromaticity axes. The radial distance from the point n on the chromaticity plane represents saturation and the location in the chromaticity plane relative to the chromaticity axes represents hue. This new coordinate system is shown relative to the R, G, B coordinate system in FIG. 1.
Traditionally, correction levels have been discussed in terms of changes along the Neutral axis N and changes along axes in a chromaticity plane.
Strictly speaking, there is only one Overall Neutral Correction Level and it represents the rate of change in the neutral components of the combined R, G, B Log Source Exposures with respect to a given change in the neutral density of an original. The Overall Neutral Correction Level is defined as: ##EQU2## where: ONC is the Overall Neutral Correction Level EQU .DELTA.log E.sub.N =7/8(.DELTA.log E.sub.R +.DELTA.log E.sub.G +.DELTA.log E.sub.B) and .DELTA.D.sub.N =7/8(.DELTA.D.sub.R +.DELTA.D.sub.G +.DELTA.D.sub.B)
however, the Overall Neutral Correction Level is commonly broken down into its Red, Green, and Blue components which are traditionally referred to as slopes and are expressed as: ##EQU3## where i takes on the values R, G, or B.
Any printer may be considered to have a unique chromaticity correction level for any arbitrary axis in a chromaticity plane. However, the most commonly considered chromaticity correction levels have been those occurring along the Red, Green, and Blue chromaticity axes and are defined as: ##EQU4## where: i takes on the values R, G, and B and log E.sub.ci and D.sub.ci are changes in log exposure and density along the respective R, G, and B chromaticity axes.
In addition, changes along an axis that lies substantially midway between the minus Red (or Cyan) and Blue chromaticity axes in the chromaticity plane have been considered. This chromaticity axes will be called the Illuminant-chromaticity axis since it is generally along this axis that color shifts occur when scene illumination is changed from tungsten to daylight. Since these color shifts are less frequently representative of scene content, it is usually desirable to have a higher correction level along the Illuminant-chromaticity axis. FIG. 2 represents a chromaticity plane showing the relationship of the Red, Green, and Blue chromaticity axes to the Illuminant-chromaticity axis. Extensions of the R, G, and B axes are labeled C, M, and Y respectively to represent the subtractive primary colors cyan, magenta, and yellow.
The chromatic correction levels along the Illuminant-chromaticity axis can be calculated from the correction matrix [A] of a settable matrix printer, but are usually determined empirically by printing a test patch or set of patches that vary from an average along the Illuminant-chromaticity axis. The patches are printed in a "locked beam" (i.e., correction matrix disabled) and in a "normal" (correction matrix in effect) mode and the resulting prints compared by densitometry to see how much correction has taken place.
Since most amateur photographic cameras operate with a fixed aperture and shutter speed i.e., they do not incude automatic exposure control, a large percentage of the pictures taken with such cameras are either under or over exposed. Thus, in any given population of originals taken by amateur photographers, by far the largest number of unwanted variations in the originals occur along the Neutral axis. For this reason, a relatively high Overall Neutral Correction Level is generally desirable. The next most frequent unwanted variation in originals taken by amateur photographers occurs along the Illumiant-chromaticity axis and is due to the fact that when film that is balanced for daylight exposure is exposed indoors under tungsten illumination, the colors in the original will be shifted along the illuminant axis with the resulting print appearing too warm. The reverse of this problem occurs when film balanced for tungsten illumination is exposed in daylight. Thus, a relatively high Illuminant-chromaticity correction level is generally desirable.
The Green-chromaticity axis is mutually perpendicular to both the neutral axis and the Illuminant-chromaticity axis. Since green-grass subject failure is a common occurrence in negative populations, it is often desirable to adjust the correction level along the Green-chromaticity axis. For the reasons noted above, it is often desirable to adjust the Neutral, Illuminant-chromaticity, and Green-chromaticity correction levels in settable matrix printers.
According to prior art methods, the Red, Green, and Blue-Neutral and Red, Green, and Blue-Chromaticity correction levels have been computed from the elements of the correction matrix [A] in the following manner: ##EQU5## where NC.sub.i are the Red, Green, and Blue Neutral Correction Levels, ONC is the Overall Neutral Correction Level and a.sub.ij are elements of correction matrix [A].
and EQU CC.sub.i =2/3a.sub.ii -7/8(a.sub.ij +a.sub.ik +a.sub.ji +a.sub.ki)+1/6 (a.sub.jj +a.sub.kk +a.sub.jk +a.sub.kj) (9)
where:
When it was desired to modify the correction matrix [A] to change correction levels, a change matrix [Q] was constructed according to some empirically derived rules outlined below. The old correction matrix [A] was multiplied on the right by the change matrix [Q] to yield the new correction matrix. EQU [A].sub.new =[A].sub.old [Q] (10)
For independent adjustment to all Red, Green, and Blue correction levels, the following rules were applied to generate the elements q.sub.ij of the change matrix [Q]: EQU diagonal elements q.sub.ii =0.222(5X.sub.i -X.sub.j -X.sub.k -1.5Y.sub.i) (11) ##EQU7## where: Z.sub.i --is the ratio of the new chromaticity correction level to the old chromaticity correction level ##EQU8## Y.sub.i --is the ratio of the new neutral correction level to the old neutral correction level ##EQU9##
and i.noteq.j.noteq.k, each taking on the value of R, G, or B. Some control over the Illuminant-chromaticity correction level was exercised by relating the Illuminant-chromaticity correction level to the Red, Green, and Blue chromaticity correction levels by the formula: EQU CC.sub.I =2/3(CC.sub.R +CC.sub.B)-7/8CC.sub.G.
where CC.sub.I is the Illuminant-chromaticity correction level.
From the above, it can be seen that, at most, 6 parameters (the 3 neutral correction levels NC.sub.i and 3 chromaticity correction levels CC.sub.i) were used to define changes to all nine elements of the correction matrix [A].
There was an inherent limitation in the prior art method of modifying the correction matrix [A] since the combination of 6 correction levels does not uniquely define a correction matrix [A]. Different correction matrices having different relationships between the off-diagonal elements (a.sub.ij, i.noteq.j) may produce identical values for the six correction levels defined above. These differences in the off-diagonal elements of different correction matrices having identical correction levels result in hue shifts in the resulting prints. These hue shifts have been intuitively discussed in the prior art in terms of color "rotations". However, in the prior art methods known to the inventor, there has not been a means for precisely quantifying and exactly controlling these color rotations when changing correction levels in settable matrix printers.